Calculating Short-Circuit Current During Logic Transitions

In this lesson, you will learn how to quantify the transient "shoot-through" current that occurs when both the PMOS and NMOS transistors in a CMOS inverter conduct simultaneously during a logic transition.

The Short-Circuit Phenomenon

In an ideal CMOS inverter, one transistor is always "off" when the other is "on," ensuring no direct path exists from the supply voltage ($V_{DD}$) to ground ($V_{SS}$). However, during a signal transition—specifically when the input voltage ($V_{in}$) is between the threshold voltages of the PMOS ($V_{tp}$) and NMOS ($V_{tn}$) transistors—both devices operate in the saturation region for a brief window. This creates a temporary, low-resistance path, resulting in a spike of short-circuit current ($I_{sc}$).

Modeling the Transient Current

The magnitude of $I_{sc}$ is primarily a function of the input rise/fall time ($t_r$ or $t_f$) and the load capacitance. If the input signal changes slowly, the transistors remain in the conducting region for a longer duration, significantly increasing the current spike. We can approximate the average short-circuit current during a transition as:

// Simplified estimation of I_sc for a single transition
// I_sc_avg = (beta/12) * (V_dd - V_tn - |V_tp|)^3 * (t_rise / T_cycle)
float calculate_isc(float beta, float vdd, float vtn, float vtp, float tr, float t_period) {
    float voltage_swing = vdd - vtn - fabsf(vtp);
    float isc_avg = (beta / 12.0f) * powf(voltage_swing, 3) * (tr / t_period);
    return isc_avg;
}

Impact on Power Management

While dynamic switching power (charging and discharging load capacitance) often dominates in high-frequency designs, short-circuit power becomes non-negligible when:

1. Slow Input Edges: Signal degradation or high-impedance routing increases transition times.
2. Low Load Capacitance: If the output load is small, the short-circuit current can account for up to 20% of total dynamic power dissipation.

To mitigate this, hardware designers prioritize fast edge rates (e.g., via buffer insertion) to minimize the time window where both transistors are partially conducting. In your embedded systems analysis, recognize that these spikes contribute to thermal stress and power budget overflows, even if the logic state itself is stable.

Key Takeaway: Short-circuit current is a transient power loss occurring during the transition window where $V_{tn} < V_{in} < V_{DD} - |V_{tp}|$; its magnitude is directly proportional to the input slope and the transconductance of the CMOS pair.